Structure of Rademacher subspaces in Cesàro type spaces

The structure of the closed linear span 𝓡 of the Rademacher functions in the Cesàro space $Ces_{∞}$ is investigated. It is shown that every infinite-dimensional subspace of 𝓡 either is isomorphic to l₂ and uncomplemented in $Ces_{∞}$, or contains a subspace isomorphic to c₀ and complemented in 𝓡. The situation is rather different in the p-convexification of $Ces_{∞} $ if 1 < p < ∞.